We did the tour of Vatican museums before it opened to the public and it was worth it for it being less busy. When we did the coliseum, we did the tour with the third tier and underground which was good. Went to the top of the 'wedding cake' building and the view was brilliant. Castel St'angelo tour including secret passage was great. St Peters basilica is stunning inside.
We went to a Lazio match at the Stadio Olimpico and loved that...sat next to their ultras and they're a bit mental. We got the train out to Ostia Antica to see the Roman remains there and loved that too.
If you can, go to Trastevere for food one night. Proper Italian atmosphere, less touristy when we were there compared to other areas and food was lush! Oh and there's the view over the city through the keyhole which is beautiful too. It's an amazing city! Obvs Trevi fountain, Pantheon and Piazza Navona etc too!